The electromagnetic (radio) spectrum is a scarce and precious resource whose efficient use is crucial for present and future wireless communication systems. Fourth-generation wireless systems already target very high per-user data rates. The goal of future transmission systems is not necessarily to increase it, but rather to achieve increased spectral efficiencies in order to be able to deliver higher aggregate data rates to larger numbers of simultaneously communicating users.
Multiple Access (MA) schemes are used to make a shared communication channel simultaneously available to several users or data streams. Next generation wireless systems will have to face the demand for higher aggregate data rates while being capable of providing reliable communication to many simultaneous users and/or applications. Such high data rates will be achieved by an increasingly efficient use of the channel's physical resources.
It would be beneficial to devise non-orthogonal schemes that achieve higher aggregate spectral efficiencies while in the same time have SNR losses as small as possible with respect to the single-stream performance. Additionally, such schemes should outperform the best cellular systems (e.g., LTE) in terms of spectral efficiency for a given amount of assigned resources.
TCMA, with its low single-user SNR loss, is a very promising technique. However, its aggregate SE is still far from the AWGN channel capacity, especially when the number of streams is high.
Overloading is a paradigm according to which, in a transmission system, several data streams are multiplexed onto the same time-frequency-space Resource Elements (RE), thus resulting in increased data rates. Applying the overloading concept to the MA context, Overloaded Multiple Access (OMA) schemes have been conceived which are able to provide significantly higher Spectral Efficiency (SE) than conventional MA schemes.
Based on the Domain of Separation (DoS) of users/streams, the following classification of OMA schemes can be made:                1) Power DoS: e.g. Non-Orthogonal Multiple Access (NOMA) schemes. Here, a far user and a near user are multiplexed on the same time-frequency-space REs. The scheme is based on the transmission of superposed signals with different amplitudes.        2) Constellation DoS: e.g., Constellation Expansion Multiple Access (CEMA). Here, subsets of constellation symbols are allocated to different users/streams.        3) Spreading Sequences DoS: e.g., Low Density Spread (LDS) CDMA, LDS-OFDM. These schemes are based on the allocation of different sparse sequences to different users/streams.        4) Spread Superposition Codebooks DoS: e.g., LDS-CDMA, LDS-OFDM, Sparse Coded Multiple Access (SCMA), Interleave-Division Multiple Access (IDMA). These schemes are based on user-specific spreading and modulation codebooks that aim to maximize the minimum Euclidean distance between the sparse spread signals of different users/streams.        5) Non-Spread Superposition Codebooks DoS: e.g., Trellis Coded Multiple Access (TCMA). This scheme is based on Trellis-Coded Modulation (TCM) with stream-specific interleaving, resulting in stream-specific non-spread codebooks.        
The increased SE of any OMA scheme is achieved at the expense of increased required transmit power for each multiplexed stream/user, in order to mitigate the degradations caused by the non-ideal performance of the multi-stream detector in the receiver. This increase of transmit power can be characterized by the so-called single-stream Signal-to-Noise Ratio (SNR) loss, a feature that is defined as a function of the aggregate Spectral Efficiency (SE) which is defined asSE(K)=(1−BLER)Rm0K [bits/s/Hz].  (1)
Here, BLER indicates the block error rate, R is the channel code rate, m0 is the modulation order in bits per symbol and K is the overloading factor, which coincides with the number of streams in TCMA systems. The spectral efficiency is a function of the SNR: we indicate withSE∞(K)=limSNR→∞SE(K)  (2)the Asymptotic Aggregate Spectral Efficiency (ASE). The relevant metric we take into account for evaluation is the single-stream SNR loss ΔSNR(K, ρ), which is the increase of SNR with respect to the single-stream SNR required by the receiver to achieve a given ratio ρ of the ASE when the overloading factor is K>1.ΔSNR(K,ρ)=SNR(SE(K)=ρSE∞(K))−SNR(SE(1)=ρSE∞(1)).  (3)
In FIG. 1, the normalized SE (SE(K)/SE∞(K)) of the TCMA scheme is shown as well as the single-stream SNR losses ΔSNR(K, ρ) for p=0.9 and K=2, . . . , 7. Table 1 summarizes the single-stream SNR losses ΔSNR(K, 0.9) of the TCMA system.
TABLE 1Single-stream SNR loss of the TCMA schemeKΔSNR (K, 0.9)2 0.6 dB3 3.4 dB4 6.75 dB510.45 dB614.25 dB7 18.8 dB
The aforementioned OMA techniques have been evaluated and compared. The resulting considerations are summarized in Table 2. We observe that, among the considered systems, TCMA is the one that features the smallest single-stream SNR loss. In fact, when K=2 streams are concurrently transmitted, its SE is close to the single-stream case (K=1) within a single-user SNR loss of 0.6 dB. Moreover, for K>2 the single-stream SNR loss is moderate. Such attractive characteristic makes TCMA schemes the best candidates for further development.
TABLE 2Comparison of known overloaded multiple access schemesProsConsNOMALow complexityOnly two users/streams, withlarge SNR gap between themas the major prerequisiteApplicable only on DLCEMARelatively small single userLimited flexibility (number ofSNR lossusers is function of availableLow complexityconstellation sizes and userdata/code rates)Applicable only on DLLDS-Moderate MUD complexityModerate single user SNRCDMAApplicable both on UL andlossDLBackward-compatible on DLSCMAModerate MUD complexityNot backward compatibleApplicable both on UL andSimilar single user SNR lossDLas in LDS-CDMADifficult to designtransmission codebooks whenloads are larger than 1.5TCMASmallest single-stream SNRReceiver complexityloss for the two-stream caseNot backward-compatibleApplicable both on UL andDL
TCMA schemes have been proposed in the UL context, where multiple devices (e.g., User Equipments, UEs) concurrently transmit their encoded, modulated and interleaved data streams. Each device transmits one data stream and all transmissions are simultaneous, i.e., the same time-frequency-space REs are used by all devices. It is also assumed that all transmissions are symbol-synchronous and that ideal power control is implemented, such that all user signals have the same average power when they reach the receiver antenna.
Each stream is independently encoded and modulated using the well-known Trellis-Coded Modulation (TCM) scheme. Before transmission, the modulated symbols are interleaved according to a stream-specific permutation.
In TCMA, each stream may be encoded and modulated using different trellis codes and modulation schemes; these stream-specific features help the receiver to separate the information belonging to different streams. However, most effective feature for stream separation is the use of stream-specific interleavers.
A scheme representing the TCMA transmission concept is shown in FIG. 2, where stream-specific interleavers are indicated with Π. Further FIG. 3 shows an example of TCM encoder-modulator consisting of a four-state convolutional encoder connected to a QPSK symbol mapper.
Thanks to the linear characteristic of the wireless channel, the received signal is the sum of concurrently transmitted signals. It is a task of the receiver to separate the signals belonging to different streams, then to perform demodulation and decoding and finally delivering the information to recipients.
An iterative TCMA receiver has been proposed in the art. Although featuring a rather high complexity, such receiver results in a good performance. Nevertheless, as will be shown in the following, the performance of the resulting scheme still exhibits a large gap with respect to the AWGN channel capacity.
FIG. 4 shows the block scheme of a TCMA receiver according to prior art. The received signal (4) is the sum of the transmitted signals, plus additive white Gaussian noise w(l):
                              r          ⁡                      (            l            )                          =                                            ∑                              k                =                0                                            K                -                1                                      ⁢                                                  ⁢                                          e                                  j                  ⁢                                                                          ⁢                                                            θ                      k                                        ⁡                                          (                      l                      )                                                                                  ⁢                                                s                  k                                ⁡                                  (                  l                  )                                                              +                      w            ⁡                          (              l              )                                                          (        4        )            where the coefficients ejθk(l) are introduced to model carrier phase and frequency offsets between different transmitters. Motivated by the presence of interleavers in the transmission system, coefficients ejθk(l) have been assumed to exhibit a uniformly distributed random phase.
In the TCMA receiver, the TCM decoders and Multi Stream Detector (MSD) interact through the interleavers in an iterative fashion by exchanging soft information referred to coded bits dk(1)(l) and dk(2)(l). Such soft information may consist of probability distributions, logarithms of probability distributions, Likelihood Radios (LRs) or Logarithms of Likelihood Ratios (LLRs). In the following, a brief description of the MSD will be given using probability distributions.
The task of the MSD consists in the separation of information belonging to different streams. The MSD computes the joint probability distribution P(d(l)|r(l))=P(d0(1)(l), d0(2)(l), . . . , dK-1(1)(l), dK-1(2)(l)|r(l)), a task whose complexity grows exponentially with the number of streams K. In fact, the domain of such function is d(l)ϵ{0,1}2K.
At each iteration and for each k-th stream, the MSD computes the marginal probabilities gk(1)(l)=P(dk(1)(l)=0|r(l)) and gk(2)(l)=P(dk(2)(l)=0|r(l)) and sends them to the TCM decoder through the deinterleaver Πk−1.
The TCM decoder updates such probabilities according to the TCM code constraints. Typically, an algorithm that operates according to the trellis of the corresponding convolutional encoder is executed. Well known algorithms for trellis decoding include the Viterbi algorithm and the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. The TCM decoder obtains improved probabilities hk(1)(l) and hk(2)(l) referred to coded bits dk(1)(l) and dk(2)(l) and feeds them back to the MSD through the interleaver Πk. Finally, the MSD uses these improved probabilities to update its joint probability distribution P(d(l)|r(l)).
The most popular multi-stream receiver algorithms perform iterative detection and decoding in a parallel or successive (serial) fashion. It is recognised that successive approaches perform better than the parallel. The Iterative Detection and Decoding (IDD) algorithm used in TCMA is described in the flowchart of in FIG. 5, where r=(r(1), . . . , r(L)) indicates the received signal, Nit indicates the number of iterations and K is the number of streams.
Using the iterative IDD algorithm at the receiver, the aggregate spectral efficiency of TCMA has been estimated (see FIG. 6, where the capacity of the Additive White Gaussian Noise (AWGN) channel is given as a reference). We observe that, although the two-stream SE exhibits very low SNR loss with respect to the single-stream SE, adding further streams results in an increased single-stream SNR loss. Moreover, the SNR gap with respect to the AWGN channel capacity increases with the number of streams: using K=7 streams, such gap approaches 12 dB.